On the Quot scheme ${\mathrm{Quot}}_S^l(\mathcal{E})$

Abstract

We study the geometry of the Quot scheme ${\mathrm{Quot}}_S^l(\mathcal{E})$ of length $l$ coherent sheaf quotients of a locally free sheaf $\mathcal{E}$ on a smooth projective surface $\mathrm{S}$. In particular, we investigate the nature of its singularities, its intersection theory, and the cohomology of sheaves on ${\mathrm{Quot}}_S^l(\mathcal{E})$.

Published version